Background to Cosmology: The Ancient Greeks

Plato's Views on the Cosmos

The ancient Greeks developed, over a period of centuries, an elaborate cosmology. By cosmology is meant the structure and the origin of the universe. The earliest views, going back to the time of Homer and Hesiod (the 8th century BC) postulated a flat or cylindrical earth located in a hemispherical cosmos that surrounded or envelopped it. But by the time of the thinkers associated with the legendary and mythical Pythagorus (560-480BC, app.), the view became widely accepted that the earth was a sphere in a universe which was itself also fully spherical. This claim was based both on theoretical grounds -- (i) the belief that the circle or sphere was the most perfect of geometric shapes, and therefore appropriate for the earth and the cosmos, which were the most important of objects, and (ii) on practical grounds -- the observations of a ship and its mast as the vessell receded beyond the horizon. Moreover, it was possible for the ancient Greeks to calculate the diameter of the earth (and therefore its circumstances) through trigonometric considerations. This was done by Eratosthenes, a Greek living in Alexandria, Egypt, around 230BC, and (depending on how his unit of length is interpreted) was accurate to within 5% of current measurements.

Plato (427-347 BC), in his later work entitled Timaeus sketched out a theory of the origin and nature of the cosmos. The world was the creation of a "Demiurge" (from the Greek "demos" or people and "ourgos" or work) -- the most highly placed of gods, working in the "public" interest (Plato, like the ancient Greeks generally, was a polytheist -- a believer in many gods). This superior god was by nature good, and so tried to create an image of itself that was as good as possible. But the Demiurge could not create a world out of nothing; its powers were more limited than the God of Genesis. The Demiurge fashioned the cosmos out of materials provided by a pre-existing "chaos", or jumble of matter, which the Demiurge organized into the four elements -- Earth, Water, Air and Fire. These formed the "body" of the cosmos, which was also endowed with a "soul". The soul of the cosmos, which Plato considered as its better or more important part, was its principle of eternal and recurring circular motion, bringing about the circular motion of the moon, planets, sun and stars.

It is presumed, though not explicitly stated by Plato, that the Earth is the center of the cosmos, with the other heavenly bodies rotating about it. (Other interpretations of Plato are possible, and we will see later that Copernicus attempted to do just this, though his was a controversial interpretation of Plato). It was Aristotle (384-322 BC) who made explicit the proposition that the earth is the center and does not move, with the sun as well as the moon, planets and stars circling it.

Aristotle's Views on the Cosmos

Aristotle based himself on various observations evident to the unaided eye (there were no telescopes in ancient Greece): (i) We see the sun "rise" and "set" each day; (ii) We don't feel that the earth moves under our feet; (iii) We see the stars describe a semi-circle about the horizon each night. All of these seem to imply that the earth is fixed at the center and the sun moves around it. Moreover, (iii) from a cultural point of view, it seemed appropriate that the earth -- the planet we inhabit -- be at the center, since after all, aren't humans (and for Aristotle, the Greeks) the most important part of the cosmos?

Aristotle accepted the four Platonic elements of Earth, Water, Air and Fire as the basis for phenomena on both the Earth (the planet) and in the atmosphere, but he added a fifth element -- known as "aether" -- as the matter of the heavenly bodies (moon, planets, sun, and stars). The motion of the aether, unlike that of the other four elements, had neither beginning nor end, and so must be circular, he reasoned, since the circle has neither beginning nor end. We can distinguish the primary elements of the theory as follows:

• (i) The earth as the center of the cosmos and does not move ("geocentrism")
  
  
• (ii) The sun moves around the earth and is not its center ("heliodynamism")
  
  
• (iii) Heavenly motions are circular (or spherical, in three dimensions)

Problems and Attempts at Solutions

Aristotle's theory became "canonical", or widely accepted as authoritative and definitive for nearly 2000 years -- until the time of Copernicus and his successors. But there were problems with the theory as expressed above, particularly as concerns the orbits of the sun and the planets, which did not seem to describe a perfect circle (by naked eye observation, using at most a sighting post). Among the problems were the following:

• (i) At periodic times, the planets seemed to reverse their direction of motion around the earth -- which is technically known as "retrograde" motion.
  
  
• (ii) Planets sometimes seemed brighter and sometimes less bright, which was interpreted to mean that they are sometimes closer and sometimes further from the earth.
  
  
• (iii) The solar seasons were not quite equal, as should be expected for perfectly circular motion. It seemed that the sun was speeding up and slowing down at various points in its orbits.

The idea is the following: the mathematical theory is constrained, for metaphysical reasons, to using only spheres, the most perfect solid, and strictly uniform motion, which is the most perfect motion. But it must account for the retrograde motions of the planets, which cannot be done with just one sphere for each planet, since that sphere must turn uniformly. According to Simplicius (a commentator on Aristotle on ancient philosophy of later antiquity), Plato set his students the following problem: basing themselves only on uniform circular motions, to "save the phenomena", ie derive curves that would correspond with the observed movements of the planets (the phenomena). The project of "saving the phenomena" dominated cosmology until the time of Newton, and has the following components:

• (i) Basic assumption: All heavenly bodies move in circular motions or motions compounded out of circles. The circle (in three dimension, the sphere) is the most perfect of geometric figures, since each point on the circumference is equidisant from the center, and the only curve appropriate to the movement of the heavenly bodies.
  
  
• (ii) Empirical observation: But the heavenly bodies (with the exception of the stars, which appear always to move in simple circular motion about the earth) do not demonstrate simple circular motions - inlcuding the phenomena of retrograde motion, varying brightnesses, and varying velocities.
  
  
• (iii) Mathematical hypotheses: Now, the basic assumption must be maintained (for intellectual reasons) and the empirical observations must be maintained as well (for practical reasons: theory must meet the test of observation). Consequently, Plato's question of "saving the phenomena" became: what types of mathematical hypotheses can be fashioned using only circles and motions compounded out of circles, in order to produce geometrical paths which approximate the observed motions.

Eudoxus (408-355 BC) was a student of Plato's who attempted a model made up of concentric spheres. Each planet was sandwiched between spheres moving at different rates in different directions, producing changes in direction equivalent to retrograde motions. But the scheme, amplified by Aristotle to include more than two spheres for each planet, was unsuccessful, as it did not explain the phenomena of varying brightness of the planets. A satisfactory solution was produced only later, through the methods of epicycles, eccentrics, and equants:

(1) Appolonios (262-190 BC) developed a first mathematical method known as "epicycles". In this method, a planet orbits a circle whose center is itself on a second circle. The first circle (the "epicycle") moves in one direction, the second circle (the "deferent") in the opposite, producing as a result motion similar to retrograde motion.

(2) A second method which gives equivalent results was that of "eccentrics", where the center of motion of a planet was at a distance from the earth (which nonetheless remained the "true" center of the cosmos as a whole). This produced planetary motion at unequal distances from the earth, helping to explain the fact that planets sometimes appear brighter and sometimes less bright, with brighter appearance interpeted as closer position. (It can be proved mathematically that the epicycle and eccentric methods give equivalent results).

(3) A third method was developed by Ptolemy (100-170 AD), a Greek speaker who lived in Alexandria, in Egypt. Technically more complicated than either of the two above, it can be understood as follows for the case of the sun: The sun moves on an earth-centered circle, but at an irregular rate determined by the condition that its rate of rotation be uniform with respect not to its own geometric center, but with respect to an equant point some distance from the geometric center. In this way, the unequal solar seasons could be explained.

The combination of these three methods (epicycle, eccentric, and equant) enabled Ptolemy to mimic in his theory the observed motions of the planets, moon and sun, including the phenomena of retrograde motion, variable brightness, and variable speed. For decades and indeed centuries the theory, contained in his book "Almagest" (Arabic for "The Greatest") enabled accurate predictions to be made.

But the theory had its weaknesses. The number of epicycles, eccentrics, and equants used was "ad hoc" -- just enough were used to obtain the desired result, but there was no way of knowing in advance how many were required. Moreover, over a thousand years (by the time of Copernicus), the predictions of the theory were out of phase with observations. We will return to this point next unit in looking at the reasons that led Copernicus to his new theory.

Views of the Cosmos of Epicurus and Lucretius

But even in the ancient world there were dissenting, if minority voices. Epicurus (342-271 BC) in his atomistic theory upheld the following propositions, in opposition to both Plato and Aristotle:

• (i) The basic units of matter are not the four or five elements of Plato and Aristotle, but much larger number of different kinds of atoms, which combine to form compounds. The atoms can neither be created nor destroyed, but the things they compose have both beginings and ends.
  
  
• (ii) The cosmos consists of many different worlds, randomnly formed by the collision of atoms, not just the one earth-centered world of Aristotle. These worlds, endless in number, also have beginnings and ends; they are not eternal.
  
  
• (iii)The cosmos is infinite in extent and therefore cannot be spherical in shape. Like the atoms of which it is solely composed (along with the void through which the atoms move), the cosmos has neither beginning nor end, either in time or in space.
  
  

This view, associated with a materialist perspective on life and death, was most clearly expressed in the epic poem of Lucretius (d. 55BC), The Nature of the Universe, and represented a radical departure from the traditional views of Plato and Aristotle, which latter enjoyed great popularity and near universal assent.

Finally, it should be noted that Aristarchus, in the third century BC, proposed (in a work now lost) that the sun, not the earth was the center of the universe. He shared the view of Aristotle and Plato that the cosmos, consisting of just one world, was spherical in shape and had a definite center (unlike Epicurus and Lucretius mentioned above). But he differed from both Plato and Aristotle in exchanging the roles of sun and earth. This will be especially relevant as we examine Copernicus in the next unit.